Answer:
[tex]y=\frac{7}{2}x-20[/tex]
Step-by-step explanation:
Let the equation of the line be [tex]y-y_1=m(x-x_1)[/tex] where, 'm' is its slope and [tex](x_1,y_1)[/tex] is a point on it.
Given:
The equation of a known line is:
[tex]y=-\frac{2}{7}x+9[/tex]
A point on the unknown line is:
[tex](x_1,y_1)=(4,-6)[/tex]
Both the lines are perpendicular to each other.
Now, the slope of the known line is given by the coefficient of 'x'. Therefore, the slope of the known line is [tex]m_1=-\frac{2}{7}[/tex]
When two lines are perpendicular, the product of their slopes is equal to -1.
Therefore,
[tex]m\cdot m_1=-1\\m=-\frac{1}{m_1}\\m=-\frac{1}{\frac{-2}{7} }=\frac{7}{2}[/tex]
Therefore, the equation of the unknown line is determined by plugging in all the given values. This gives,
[tex]y-(-6))=\frac{7}{2}(x-4)\\y+6=\frac{7}{2}x-14\\y=\frac{7}{2}x-14-6\\\\y=\frac{7}{2}x-20[/tex]
The equation of a line perpendicular to the given line and passing through (4, -6) is [tex]y=\frac{7}{2}x-20[/tex].
